Answer:
Rate of boat in still water = 105 mph
Rate of current = 15 mph
Explanation:
Let the speed of the boat in still water be [tex]v_b[/tex].
Let the speed of the current be [tex]v_c[/tex].
When the boat goes upstream, it moves against the current. Hence, its velocity will be relative to that of the current. This is given by 360/4 = 90 mph.
This relative velocity is the difference between the speed of the boat in still water and that of the current:
[tex]v_b - v_c = 90[/tex]
In the downstream, the boat moves with the current. The resultant velocity is the sum of the velocities of boat in still water and current.
[tex]v_b+v_c = 360/3 =120[/tex]
Solving both equations simultaneously by elimination method,
[tex]2v_b = 210[/tex] (adding both equations)
[tex]v_b = 105\text{ mph}[/tex]
[tex]2v_c = 30[/tex] (subtracting the first from the second equation)
[tex]v_c =15\text{ mph}[/tex]
